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Polynomial interpolation

Interpolation finds a polynomial that passes exactly through a set of points, and is used to estimate values between them. A polynomial of degree $n$ is uniquely determined by $n+1$ points. With many evenly spaced points, high-degree polynomials can oscillate strongly near the ends — Runge's phenomenon.

n+1

number of points that determine an interpolating polynomial of degree

n

Symbols

n

the degree of the polynomial

Example

Linear interpolation between $(1, 1)$ and $(5, 1)$ gives $y = 1$ for all $x$ in between, since both points have the same $y$ .

Avoid high-degree interpolation at evenly spaced points — use Chebyshev points or splines instead.

Practise interpolation and integration for free →

← Simpson's rule · Splines and Gaussian quadrature →

Part of Numerical Methods: Interpolation and integration.